Wave on a guitar string

A guitar string is vibrating in its fundamental mode, with nodes at each end. The length of the segment of the string that is free to vibrate is L. The maximum transverse acceleration of a point at the middle of the segment is a and the maximum transverse velocity is v.

What is the amplitude of this standing wave?

I worked out the fundamental frequency, which I think is v/2L, but I'm not sure how to get A, since all of the formulae that I know relating to A involve k.